{"id":2766,"date":"2023-09-23T15:45:18","date_gmt":"2023-09-23T06:45:18","guid":{"rendered":"http:\/\/mepa.jsiam.org\/?page_id=2766"},"modified":"2023-12-07T19:11:17","modified_gmt":"2023-12-07T10:11:17","slug":"%e6%97%a5%e6%9c%ac%e5%bf%9c%e7%94%a8%e6%95%b0%e7%90%86%e5%ad%a6%e4%bc%9a%e3%80%8c%e8%a1%8c%e5%88%97%e3%83%bb%e5%9b%ba%e6%9c%89%e5%80%a4%e5%95%8f%e9%a1%8c%e3%81%ae%e8%a7%a3%e6%b3%95%e3%81%a8%e3%81%9d","status":"publish","type":"page","link":"http:\/\/mepa.jsiam.org\/?page_id=2766","title":{"rendered":"\u65e5\u672c\u5fdc\u7528\u6570\u7406\u5b66\u4f1a\u300c\u884c\u5217\u30fb\u56fa\u6709\u5024\u554f\u984c\u306e\u89e3\u6cd5\u3068\u305d\u306e\u5fdc\u7528\u300d\u7814\u7a76\u90e8\u4f1a \u7b2c36\u56de\u7814\u7a76\u4f1a"},"content":{"rendered":"\n<p>\u65e5\u672c\u5fdc\u7528\u6570\u7406\u5b66\u4f1a\u300c\u884c\u5217\u30fb\u56fa\u6709\u5024\u554f\u984c\u306e\u89e3\u6cd5\u3068\u305d\u306e\u5fdc\u7528\u300d\u7814\u7a76\u90e8\u4f1a\u3067\u306f\uff0c\u7b2c36\u56de\u7814\u7a76\u4f1a\u3092\u958b\u50ac\u81f4\u3057\u307e\u3059\uff0e<\/p>\n\n\n\n<ul>\n<li><strong>\u958b\u50ac\u65e5\uff1a2023\u5e7412\u67088\u65e5\uff08\u91d1\uff09<\/strong><\/li>\n\n\n\n<li><strong>\u4f1a\u5834\uff1a\u30aa\u30f3\u30e9\u30a4\u30f3\uff08Zoom\uff09<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\u30aa\u30f3\u30e9\u30a4\u30f3\u958b\u50ac\u306e\u305f\u3081\uff0c\u4e8b\u524d\u767b\u9332\u5236\u3068\u3055\u305b\u3066\u9802\u304d\u307e\u3059\uff0e\u53c2\u52a0\u30fb\u8b1b\u6f14\u3092\u5e0c\u671b\u3055\u308c\u308b\u65b9\u306f\u4e0b\u8a18\u306e\u300c\u53c2\u52a0\u7533\u3057\u8fbc\u307f\u30d5\u30a9\u30fc\u30e0\u300d\u30fb\u300c\u8b1b\u6f14\u7533\u3057\u8fbc\u307f\u30d5\u30a9\u30fc\u30e0\u300d\u3088\u308a\u767b\u9332\u3092\u304a\u9858\u3044\u81f4\u3057\u307e\u3059\uff0e\u4e21\u30d5\u30a9\u30fc\u30e0\u306f\u72ec\u7acb\u3057\u305f\u3082\u306e\u3067\u3059\u306e\u3067\uff0c\u8b1b\u6f14\u3092\u3054\u5e0c\u671b\u306e\u5834\u5408\u306f\uff0c\u8b1b\u6f14\u7533\u3057\u8fbc\u307f\u3068\u306f\u5225\u9014\uff0c\u53c2\u52a0\u7533\u3057\u8fbc\u307f\u3082\u304a\u9858\u3044\u81f4\u3057\u307e\u3059\uff0e\u8b1b\u6f14\u6642\u9593\u306f\uff0c\u8cea\u7591\u5fdc\u7b54\u3092\u542b\u3081\u306620\u5206\uff5e30\u5206\u3092\u4e88\u5b9a\u3057\u3066\u3044\u307e\u3059\uff08\u5168\u4f53\u306e\u8b1b\u6f14\u6570\u3092\u8e0f\u307e\u3048\u3066\u6c7a\u5b9a\u81f4\u3057\u307e\u3059\uff09\uff0e<\/p>\n\n\n\n<p>\u672c\u7814\u7a76\u4f1a\u3067\u306e\u767a\u8868\u306b\u306f\uff0c<a href=\"https:\/\/www.jstage.jst.go.jp\/browse\/jsiaml\/-char\/ja\/\">JSIAM Letters<\/a> \u8a8c\u3078\u306e\u6295\u7a3f\u6a29\u304c\u4ed8\u4e0e\u3055\u308c\u307e\u3059\uff0e\uff08\u8457\u8005\u306b\u65e5\u672c\u5fdc\u7528\u6570\u7406\u5b66\u4f1a\u4f1a\u54e1\u304c\u542b\u307e\u308c\u3066\u3044\u306a\u304f\u3066\u3082 JSIAM Letters \u8a8c\u3078\u306e\u6295\u7a3f\u6a5f\u4f1a\u304c\u4e0e\u3048\u3089\u308c\u307e\u3059\uff0e\u6295\u7a3f\u53d7\u4ed8\u671f\u9593\u306f 2023\u5e7412\u67089\u65e5\uff5e2024\u5e7412\u670831\u65e5 \u3067\u3059\uff0e\uff09<\/p>\n\n\n\n<p>\u554f\u3044\u5408\u308f\u305b\u5148\uff1ahsato &lt;at&gt; i.kyoto-u.ac.jp\uff08\u62c5\u5f53\uff1a\u4eac\u90fd\u5927\u5b66 \u4f50\u85e4 \u5bdb\u4e4b\uff09<\/p>\n\n\n\n<p><\/p>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<h2>\u53c2\u52a0\u7533\u3057\u8fbc\u307f\u30d5\u30a9\u30fc\u30e0<\/h2>\n\n\n<div role=\"form\" class=\"wpcf7\" id=\"wpcf7-f2773-o1\" lang=\"ja\" dir=\"ltr\">\n<div class=\"screen-reader-response\"><p role=\"status\" aria-live=\"polite\" aria-atomic=\"true\"><\/p> <ul><\/ul><\/div>\n<form action=\"\/index.php?rest_route=%2Fwp%2Fv2%2Fpages%2F2766#wpcf7-f2773-o1\" method=\"post\" class=\"wpcf7-form init\" novalidate=\"novalidate\" data-status=\"init\">\n<div style=\"display: none;\">\n<input type=\"hidden\" name=\"_wpcf7\" value=\"2773\" \/>\n<input type=\"hidden\" name=\"_wpcf7_version\" value=\"5.3.2\" \/>\n<input type=\"hidden\" name=\"_wpcf7_locale\" value=\"ja\" \/>\n<input type=\"hidden\" name=\"_wpcf7_unit_tag\" value=\"wpcf7-f2773-o1\" \/>\n<input type=\"hidden\" name=\"_wpcf7_container_post\" value=\"0\" \/>\n<input type=\"hidden\" name=\"_wpcf7_posted_data_hash\" value=\"\" \/>\n<\/div>\n<p><strong>\u6c0f\u540d<\/strong><font color=\"red\">\u3010\u5fc5\u9808\u3011<\/font><br \/>\n    <span class=\"wpcf7-form-control-wrap yourname\"><input type=\"text\" name=\"yourname\" value=\"\" size=\"40\" class=\"wpcf7-form-control wpcf7-text wpcf7-validates-as-required\" aria-required=\"true\" aria-invalid=\"false\" \/><\/span> <\/p>\n<p><strong>\u6240\u5c5e<\/strong><font color=\"red\">\u3010\u5fc5\u9808\u3011<\/font><br \/>\n    <span class=\"wpcf7-form-control-wrap affiliation\"><input type=\"text\" name=\"affiliation\" value=\"\" size=\"40\" class=\"wpcf7-form-control wpcf7-text wpcf7-validates-as-required\" aria-required=\"true\" aria-invalid=\"false\" \/><\/span> <\/p>\n<p><strong>\u30e1\u30fc\u30eb\u30a2\u30c9\u30ec\u30b9<\/strong><font color=\"red\">\u3010\u5fc5\u9808\u3011<\/font><br \/>\n    <span class=\"wpcf7-form-control-wrap email-address\"><input type=\"email\" name=\"email-address\" value=\"\" size=\"40\" class=\"wpcf7-form-control wpcf7-text wpcf7-email wpcf7-validates-as-required wpcf7-validates-as-email\" aria-required=\"true\" aria-invalid=\"false\" \/><\/span><\/p>\n<p><input type=\"submit\" value=\"\u78ba\u8a8d\" class=\"wpcf7-form-control wpcf7-confirm wpcf7c-elm-step1 wpcf7c-btn-confirm 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Kadri\uff08Marseille\u5927\uff09<br>RKHM\u3068Perron-Frobenius\u4f5c\u7528\u7d20\u3092\u7528\u3044\u305f\u30ab\u30fc\u30cd\u30eb\u6df1\u5c64\u5b66\u7fd2<\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#deecf5;font-size:14px\">\u6982\u8981\uff1a\u672c\u767a\u8868\u3067\u306f\uff0cRKHM\u306e\u95a2\u6570\u3092\u8907\u6570\u5408\u6210\u3059\u308b\u3053\u3068\u306b\u3088\u308b\u30ab\u30fc\u30cd\u30eb\u6df1\u5c64\u5b66\u7fd2\u3092\u63d0\u6848\u3057\uff0c\u305d\u306e\u6c4e\u5316\u6027\u80fd\u306b\u3064\u3044\u3066\u8003\u5bdf\u3059\u308b\uff0e\u95a2\u6570\u5408\u6210\u3092\u8868\u73fe\u3059\u308b\u7dda\u5f62\u4f5c\u7528\u7d20\u3067\u3042\u308bPerron-Frobenius\u4f5c\u7528\u7d20\u3092RKHM\u4e0a\u3067\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u3067\uff0c\u5358\u72ec\u306e\u95a2\u6570\u306b\u95a2\u3059\u308b\u8b70\u8ad6\u3092\u8907\u6570\u306e\u95a2\u6570\u306e\u5408\u6210\u306b\u5bfe\u3057\u3066\u62e1\u5f35\u3059\u308b\uff0eC*\u74b0\u3084Perron-Frobenius\u4f5c\u7528\u7d20\u3092\u7528\u3044\u308b\u3053\u3068\u3067\uff0c\u4f5c\u7528\u7d20\u30ce\u30eb\u30e0\u304c\u5229\u7528\u53ef\u80fd\u3068\u306a\u308a\u95a2\u6570\u306e\u51fa\u529b\u6b21\u5143\u306b\u5bfe\u3059\u308b\u4f9d\u5b58\u6027\u304c\u4f4e\u3044\u6027\u80fd\u8a55\u4fa1\u304c\u53ef\u80fd\u306b\u306a\u308b\uff0c\u826f\u6027\u904e\u5b66\u7fd2\u3068\u306e\u95a2\u9023\u6027\u3092\u8003\u5bdf\u53ef\u80fd\u306b\u306a\u308b\uff0c\u306a\u3069\u306e\u5229\u70b9\u304c\u3042\u308b\u3053\u3068\u3092\u8b70\u8ad6\u3059\u308b\uff0e<\/p>\n\n\n\n<p>\u8b1b\u6f142\uff0814:30\uff5e14:55\uff09\uff1a\u25cb\u5409\u6fa4 \u771f\u592a\u90ce\uff08\u30c8\u30e8\u30bf\u81ea\u52d5\u8eca\u682a\u5f0f\u4f1a\u793e\uff09<br>\u78ba\u7387\u884c\u5217\u306e\u30d5\u30ed\u30d9\u30cb\u30a6\u30b9\u6a19\u6e96\u5f62\u3068\u53cd\u5c04\u578b\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\u56fa\u6709\u5024\u554f\u984c<\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#deecf5;font-size:14px\">\u6982\u8981\uff1a\u76f8\u4f3c\u5909\u63db\u306b\u3088\u3063\u3066\u5bfe\u79f0\u5316\u53ef\u80fd\u306a\u78ba\u7387\u884c\u5217\u306e\u56fa\u6709\u5024\u554f\u984c\u3092\u8003\u3048\u308b\uff0eSzegedy\u304c\u8003\u5bdf\u3057\u305f\u63a8\u79fb\u78ba\u7387\u884c\u5217\uff08\u53cd\u5c04\u578b\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af(2004)\uff09\u306b\u5bfe\u3059\u308bGoogle\u30c6\u30ec\u30dd\u30fc\u30c6\u30fc\u30b7\u30e7\u30f3\u884c\u5217\u306e\u6442\u52d5\u306b\u3088\u3063\u3066\uff0c\u63a8\u79fb\u78ba\u7387\u884c\u5217\u306e\u56fa\u6709\u5024\u53ca\u3073\u7279\u6027\u65b9\u7a0b\u5f0f\u304c\u53d7\u3051\u308b\u5f71\u97ff\u3084\uff0c\u63a8\u79fb\u78ba\u7387\u884c\u5217\u306e\u6700\u5927\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u306e\u6210\u5206\u30e9\u30f3\u30ad\u30f3\u30b0\u3078\u306e\u5f71\u97ff\u3092\u8003\u3048\u308b\uff0e<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><strong>\u7b2c\uff12\u30bb\u30c3\u30b7\u30e7\u30f3\u3000\u5ea7\u9577\uff1a<\/strong><strong>\u6a4b\u672c \u60a0\u9999\uff08NTT\uff09<\/strong>\uff0a12\/7: \u5ea7\u9577\u304c\u5909\u66f4\u3068\u306a\u308a\u307e\u3057\u305f\uff0e\u4e88\u3081\u3054\u4e86\u627f\u4e0b\u3055\u3044\uff0e<\/p>\n\n\n\n<p>\u8b1b\u6f143\uff0815:10\uff5e15:35\uff09\uff1a\u25cb\u5c71\u672c \u5b9f\u592e\uff08\u6771\u4eac\u90fd\u5e02\u5927\u5b66\uff09\uff0c\u76f8\u539f \u7814\u8f14\uff08\u6771\u4eac\u90fd\u5e02\u5927\u5b66\uff09<br>Global CG\u6cd5\u306b\u5bfe\u3059\u308b\u53ef\u5909\u7684\u524d\u51e6\u7406\u3068\u8aa4\u5deeA\u30ce\u30eb\u30e0\u306e\u53ce\u675f\u632f\u308b\u821e\u3044<\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#deecf5;font-size:14px\">\u6982\u8981\uff1aCG\u6cd5\u306f\u5927\u898f\u6a21\u304b\u3064\u758e\u306a\u6b63\u5b9a\u5024\u5bfe\u79f0\u884c\u5217\u3092\u4fc2\u6570\u3068\u3059\u308b\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u306b\u6709\u52b9\u3067\u3042\u308a\uff0c\u8907\u6570\u53f3\u8fba\u30d9\u30af\u30c8\u30eb\u3092\u3082\u3064\u5834\u5408\u3084\u4e00\u822c\u306e\u7dda\u5f62\u884c\u5217\u65b9\u7a0b\u5f0f\u306b\u5411\u3051\u3066\uff0cglobal\u578b\u3078\u306e\u62e1\u5f35\u3082\u306a\u3055\u308c\u3066\u3044\u308b\uff0e\u307e\u305f\uff0c\u524d\u51e6\u7406\u3092\u65bd\u3059\u3053\u3068\u3067\u53ce\u675f\u6027\u306f\u5927\u5e45\u306b\u5411\u4e0a\u3059\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u308b\uff0e\u672c\u7814\u7a76\u3067\u306f\uff0cglobal CG\u6cd5\u306b\u95a2\u3057\u3066\uff0c\u53ef\u5909\u7684\u524d\u51e6\u7406\u306e\u4e00\u7a2e\u3067\u3042\u308b\u201c\u53cd\u5fa9\u6cd5\u3092\u7528\u3044\u305f\u524d\u51e6\u7406\u201d\u306b\u7740\u76ee\u3057\uff0c\u305d\u306e\u524d\u51e6\u7406\u4ed8\u304d\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u7d44\u307f\u7acb\u3066\uff0c\u304a\u3088\u3073\u8aa4\u5deeA\u30ce\u30eb\u30e0\u306e\u53ce\u675f\u632f\u308b\u821e\u3044\u306b\u3064\u3044\u3066\u8003\u5bdf\u3059\u308b\uff0e<\/p>\n\n\n\n<p>\u8b1b\u6f144\uff0815:35\uff5e16:00\uff09\uff1a\u25cbKota Sugihara (no affiliation), Ken Hayami (National Institute of Informatics)<br>Right preconditioned GMRES for arbitrary singular systems<\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#deecf5;font-size:14px\">\u6982\u8981\uff1aGMRES determines a least squares solution of singular linear systems without breakdown for arbitrary right-hand side if and only if the coefficients matrix is range-symmetric. We propose a right preconditioned GMRES using the product of an SPD matrix and the transpose of the coefficient matrix. This determines a least squares solution without breakdown for arbitrary singular systems. To make the method numerically stable for inconsistent systems, we propose using pseudoinverse with an appropriate threshold parameter to suppress the influence of tiny singular values of the severely ill-conditioned Hessenberg systems arising in GMRES. Numerical experiments show that the method is effective.<\/p>\n\n\n\n<p>\u8b1b\u6f145\uff0816:00\uff5e16:25\uff09\uff1a\u25cb\u9ad8\u8c37 \u5468\u5e73\uff08\u500b\u4eba\uff09<br>\u5bfe\u79f0Deflated System\u306b\u5bfe\u3059\u308bCR\u6cd5\u306e\u9069\u7528\u306b\u3064\u3044\u3066<\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#deecf5;font-size:14px\">\u6982\u8981\uff1a\u30af\u30ea\u30ed\u30d5\u90e8\u5206\u7a7a\u9593\u6cd5\u306e\u53ce\u675f\u6027\u3092\u6539\u5584\u3059\u308b\u6280\u6cd5\u3067\u3042\u308bdeflation\u3092BiCR\u6cd5\u306b\u9069\u7528\u3059\u308b\u305f\u3081\u306e\u624b\u7d9a\u304d\u3068\u3057\u3066\u3001deflated BiCG\u6cd5\u306e\u305f\u3081\u306e\u7dda\u5f62\u65b9\u7a0b\u5f0f\u306bBiCR\u6cd5\u3092\u305d\u306e\u307e\u307e\u9069\u7528\u3059\u308b\u3053\u3068\u304c\u8003\u3048\u3089\u308c\u308b\u3002\u672c\u8b1b\u6f14\u3067\u306f\u7406\u8ad6\u7684\u691c\u8a0e\u306e\u7aef\u7dd2\u3068\u3057\u3066deflated 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